Problem:

MI6's Q Branch is developing a new ultra dry martini. The martini is a mixture of vodka plus three liquid ingredients: A, B, and C. To ensure proper performance, the total amount of additive (amount of A plus amount of B plus amount of C) must be at least 10 ounces per gallon of vodka. For safety reasons, however, the amount of additive must not exceed 15 ounces per gallon of vodka. The mix or blend of the three ingredients is critical. At least one ounce of ingredient A must be used for every ounce of ingredient B. The amount of ingredient C must be greater than one-half the amount of ingredient A. The mixture must contain at least one ounce each of A, B, and C. The cost per ounce for ingredients A, B, and C is $10, $3, and $9 respectively. The martini must be shaken, not stirred.

Required:

Question 1) provide a two sentence, layman's explanation of your results, i.e., the answer you would provide to MI6's Q Branch regarding this specific scenario.

Question 2) Explain a) the shadow prices (include the allowable increases and decreases in your discussion) and b) the allowable increase and decrease for any one of your objective function coefficients.

Provide thorough explanation of the given question.